How could we estimate the square footage of a room from an image?
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A possible approach is:


Gather many example images of rooms for which you know the square footage. Record the square footage of each room together with each image.
Pick a machine learning model that is well suited to learning relationships between images and numerical outputs, like a Convolutional Neural Network.
Train a machine learning model using an optimisation algorithm, like gradient decent. In the case of training a CNN, this algorithm starts by setting up the network with randomly chosen connection strengths between different 'simulated' neurons. It then exposes the network to an input image, and observes the number the network outputs in response. The algorithm then makes small adjustments to the strengths of the connections in the network, so that if the network were exposed to the image a second time, it would output a number that was less wrong (i.e. closer to the correct square footage). By repeating this process many thousands of times, and with many images, the network eventually becomes quite good at guessing the square footage of new images that it hasn't seen before.


In practice, the network is quite likely to pick up on any patterns in the images that correlate with square footage, not necessarily the ones you want. For example, it might pick up on, say, the fact that humans in the picture are usually a good object to guess at the scale of the rest of the room.